Stuck on a Trig-Sub

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Bvana

New member
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Nov 24, 2019
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6
Good Sunday afternoon,
I'm having issues with this Trig-Sub; I was hoping someone could help.

1574629296921.png

I am stuck on the last step, could anyone nudge me into the right direction please?
Thank you,
Benoit

Edit: for some reason, the initial equation didn't show properly.
1574629416001.png
 
If I were you I would start by using \(\displaystyle u=x^2\) and \(\displaystyle du=2xdx\) to get \(\displaystyle \frac{1}{2}\int {\frac{{du}}{{\sqrt {25 - 25{u^2}} }}} \).
Go on from there
 
This is where I got with x^2 = sin(u); is it wrong?
1574631446248.png


I'll try with u = x^2 now
 
From the u=x2 sub and then into a u=sin(teta) sub; I arrived at 1574632590303.png which was the right answer. Thank you everyone for your help.

Edit: Is there a way to close a thread when it's solved?
 
Bvana said:
This is where I got with x^2 = sin(u); is it wrong?
View attachment 14958


I'll try with u = x^2 now
Click to expand...
You made a mistake in the very beginning!

x2 = sin(u)

2 * x * dx = cos(u) du

So your integrand becomes:

\(\displaystyle \frac{1}{10} * \int{\frac{cos(u) \ du}{\sqrt{1 - sin^2(u)}}}\)

and so on.....
 
Bvana said:
Good Sunday afternoon,
I'm having issues with this Trig-Sub; I was hoping someone could help.

View attachment 14956

I am stuck on the last step, could anyone nudge me into the right direction please?
Thank you,
Benoit

Edit: for some reason, the initial equation didn't show properly.
View attachment 14957
Click to expand...
Since \(\displaystyle \sqrt(x^2) = |x|\) you really can't conclude that \(\displaystyle \dfrac{cos(x)}{\sqrt{1-sin^2(x)}} =1\) ........................ edited(II)​
 
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